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1 IMES DISCUSSION PAPER SERIES Discuss ssion Paper No. 98-J-2 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN
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3 IMES Discuss ssion Paper Series 98-J VaRVWAP [email protected] [email protected] BIS THE MEASUREMENT OF AGGREGATE RISK BIS World Wide Web WWW BIS
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5 1 Mori, Ohsawa, and Shimizu (1996) VaR Fallon (1996) Alexander (1996) VaR GARCH 1 Wilson (1996) Board of Governors of the Federal Reserve System ed. (1996) Part II Session
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7 VaR 4 4 lender of last resort
8 Glosten and Harris (1988) order-processing cost adverse selection cost Glosten and Milgrom <1985>George, Kaul, and Nimalendran (1991) AMEX/NYSENASDAQ Longstaff (1995) Black-Scholes
9 Amihud and Mendelson (1987) NYSE open-toopenclose-to-close Stoll and Whaley (1990) Lee and Lin (1995)
10 Amihud and Mendelson (1987) 5 NYSE Clark, McConnell and Singh (1992) NYSE Ritter and Chopra (1989) 5 Easley, Kiefer, O hara, and Paperman (1996)
11 parking-theproceeds Bollerslev and Melvin (1994) Bollerslev and Domowitz (1993) Glassman (1987) Locke and Sarkar (1996) readiness
12 Hebner <1996> a. b. c. d. Watanabe (1996) 6 1,
13 VaR NYSE kurtosis VWAP; volume-weighted average price) VWAP kurtosis
14 NYSE NYSE MOC; market-on-close 7 TSE VWAP VWAP VWAP 2 100,000 7 NYSE
15 8 VaR VWAP VaR VaR 1 1/ P = P exp s e t + s e ( ) ex VWAP VWAP a H b P ex 0 P VWAP s VWAP 1996 VWAP VWAP s H VWAP t e, e a b 9 ( s e ) Pbid = Pm exp m t - f( u) ( s e ) Pask = Pm exp m t + f( u) 2 P bid 0 1
16 99 VaR VaR 10 normal market size 1 11 P ask 0 P m t s m f () e u 10 VaR VaR 11
17 12 90 VaR Lee and Ready (1991) P P i bid i ask i i V g u i = Pbid æ ( ö -1 2 ) l expç- è NMS ø i i æ V g ( u ö i-1 2 ) l = Pask expç è NMS ø i P bid 0 0 Pbid = Pm exp ( s m e t) - E[ f( u1 )] 0 0 Pask = Pm exp ( s m e t) + E[ f( u1 )]
18 VaR VaR VaR herding behavior Shimizu (1997) i P ask 0 P m t s m f () g l () e u u i 1, 2 V i NMS
19 VaR Shimizu (1997)
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21 ( t ) ( t+1 ) ( t+2 ) VWAP (1929.1) VWAP (1930.5) VWAP (1982.9)
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28 Alexander, C. (1996), Volatility and Correlation Forecasting, in C. Alexander, ed., The Handbook of Risk Management and Analysis, West Sussex: John Wiley. Bollerslev, T. and I. Domowitz (1993), Trading Patterns and Prices in the Interbank Foreign Exchange Market, Journal of Finance, 4, Bollerslev, T. and M. Melvin (1994), Bid-ask Spreads and Volatility in the Foreign Exchange Market, Journal of International Economics, 36, Board of Governors of the Federal Reserve System, ed.(1996), Risk Measurement and Systemic Risk --Proceedings of a Joint Central Bank Research Conference, November 1995, Washington, D.C. Clark, R.A., J.J. McConnell, and M. Singh (1992), Seasonalities in NYSE Bid-Ask Spreads and Stock Returns in January, Journal of Finance, 5, Easley, D., N.M. Kiefer, M. O Hara, and J.B. Paperman, Liquidity, Information, and Infrequently Traded Stocks, Journal of Finance, 4, Fallon, W. (1996), Calculating Value-at-Risk, a paper presented at the Wharton Conference on Risk Management in Banking on October 13-15, George, T. J., G. Kaul, and M. Nimalendran(1991), Estimation of the Bid-Ask Spread and Its Components: A New Approach, Review of Financial Studies, 4-4, Glassman D.(1987), Exchange Rate Risk and Transactions Costs: Evidence from Bid- Ask Spreads, Journal of International Money and Finance, 6, Glosten, L.R. and L.E. Harris (1988), Estimating the Components of the Bid-Ask Spread, Journal of Financial Economics, 21, Glosten, L.R. and P.R. Milgrom (1985), Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders, Journal of Financial Economics, 14, Hebner, K. (1996), Liquidity in Financial Markets: Theory and Evidence, mimeo. Lee, J-H and J-C Lin (1995), Volatility and Liquidity at NYSE Opening Calls: A Closer Look, Journal of Financial Economics, 4,
29 Lee, C. M. and M. J. Ready (1991), Inferring Trade Direction from Intraday Data, Journal of Finance, 2, Locke P.R. and A. Sarkar (1996), Volatility and Liquidity in Futures Markets, Federal Reserve Bank of New York Research Paper No. 9612, May. Longstaff, F.A.(1995), How Much Can Marketability Affect Security Values?, Journal of Finance, 5, Mori, A., M. Ohsawa, and T. Shimizu (1996), A Framework for More Effective Stress Testing, in FRB, ed., Risk Measurement and Systemic Risk --Proceedings of a Joint Central Bank Research Conference, November 1995, Washington D.C.. Shimizu, T. (1997), Dynamic Macro Stress Exercise Including Feedback Effects, mimeo, Institute for Monetary and Economic Studies, Bank of Japan. Stoll, H.R. and R.E. Whaley (1990), Stock Market Structure and Volatility, Review of Financial Studies, 44, Watanabe, T., Intraday Price Volatility and Trading Volume: A Case of the Japanese Government Bond Futures, in FRB, ed., Risk Measurement and Systemic Risk, Washington D.C. (forthcoming). Wilson, T. (1996), Calculating Risk Capital, in C. Alexander, ed., The Handbook of Risk Management and Analysis, West Sussex: John Wiley.
IMES Discussion Paper Series 98-J
IMES DISCUSSION PAPER SERIES Discuss ssion Paper No. 98-J-1 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN IMES Discussion Paper Series 98-J-1 1998 1 E-mail: [email protected] 1. 1.1.
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